Quasi-alternating links with small determinant

Tye Lidman; Steven Sivek

doi:10.1017/s0305004116000578

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arXiv · 1507.04705

Quasi-alternating links with small determinant

Tye Lidman·Steven Sivek

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Abstract

Quasi-alternating links of determinant 1, 2, 3, and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal since there are quasi-alternating links not of this form for all larger determinants. We achieve this by studying their branched double covers and characterizing distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.

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Tye Lidman, Steven Sivek. 2015-07-16. Quasi-alternating links with small determinant. https://doi.org/10.1017/s0305004116000578

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